Why is this surface wrinkly?
Your object has very irregular topology containing triangles and ngons:



These should be avoided as much as possible when working with the subdivision surface modifier, as they will cause strange distortions like the ones you are seeing.

When working with subsurf, try to make your object completely out of evenly spaced quads (faces with four vertices):



Also try to keep the normals consistently pointing outwards, otherwise you might see dark shading artifacts. You can recalculate the normals by selecting everything (A) in edit mode (&#8633; Tab) and pressing &#9096; CtrlN.

This will result in a much smoother surface, which makes shrink wrap give the desired result:



Note that the object you are shrink-wrapping is made up of tris, so subsurf isn't advisable on it either.

Example .blend